If asked to find the work done by a varying force F(x) = 4x^3 from -4 to
+4, using integration the work done equals 0. How can it be physically
that no work is done when applying this force over a distance of 8 units?

Do reaction force and normal force mean the same kind of force? Must
the normal force always be perpendicular to the surface acted upon?
What about reaction force? If a force of, say, 10 N acts on a surface
at a 45 degree angle, what are the degrees of normal force and
reaction force? Should the normal force always be 90 degrees,
regardless of the angle of the original force?

During a test a rocket is traveling upward at 75m/s, and when it is 40 m
from the ground its engine fails. What is the maximum height reached by
the rocket, and what is its speed just before it hits the ground?

Suppose you grab the end of a chain that weights 3 lb/ft and lift it
straight up off the floor at a constant speed of 2 ft/s: determine the
force as a function of height; how much work do you do in lifting the top
of the chain 4 feet?

A student does not understand the magnitude that results from adding two vectors.
With worked examples both abstract and concrete, Doctor Ian clears up the confusion
before evoking the triangle inequality on the face of an analog clock.

A stone is thrown to hit a bird at the top of a pole. At the instant the
stone is thrown, the bird flies away in a horizontal straight line...
find the horizontal component of the velocity of the stone.